LOGIC OF BACON AND DESCARTES, modern reform of logic, by which may be understood the attempt to place logical theory in a more close and living relation to actual scientific method, begins with Bacon and Descartes. To both the scholastic logic presented itself as the essence of a thoroughly false and futile method of knowledge. Neither had the acquaintance with the genuine Aristotelian system requisite in order to distinguish the elements of permanent value from the worthless accretions under which these had been buried, and, as a natural consequence, the views of both have a far closer resemblance to the Aristotelian doctrine than might be imagined from the attitude of opposition common to them. Both thinkers were animated by the spirit of reformation in science, and both emphasize the practical end of all speculation. For both, therefore, logic, which to neither is of high value, appeared to be a species of practical science, a generalized statement of the mode in which intellect acquires new knowledge, in which the mind proceeds from known to unknown.5 But such a conception of logic is, if the expression be permitted, formal ; that is to say, the actual province of logic is not determined thereby, but awaits determination from the further idea of the nature of knowledge and the ultimate constitution of that which is to be known. When this point is reached, a radical divergence presents itself between the views of Descartes and Bacon, consequent on which appeals a radically divergent statement of the main processes and methods of logical theory.

To Descartes the ideal of cognition is the mathematical, that in which from assured and distinct data we proceed by strict sequence of proof to determine accurately and completely the nature of complex phenomena. Such an ideal, extended so as to embrace knowledge as a whole, dominates the whole of the Cartesian speculation, and, as in the case of the Socratic doctrine of knowledge, is the ground of the Cartesian doubt. Perfect certainty, i.e., clearness and distinctness of principles, logical consecutiveness of deduction from them, and exhaustive enumeration of details - such are the characteristics of completed knowledge. There follow naturally therefrom the main processes of knowledge : - intuition, by which the simple data and axioms are apprehended ; induction, or exhaustive enumeration of the elementary factors of any phenomenon ; deduction, or determination of the complex as the necessary result of the combination of simple factors. To the processes of induction and deduction, when viewed more generally, the titles analysis and synthesis may be given.' On other portions of logical theory Descartes does not enter, and the text-books of the Cartesian school, even the celebrated Port Royal logic, do little more than expound with some freshness such of the older material as seemed capable of harmonizing with the new conception.

Two things only require note in respect to the Cartesian logic, apart from its freshness and completeness ; the one is the obscurity which hangs over the nature of intuition ; the other is the step in advance of the scholastic logic effected in the assimilation of deduction to synthesis. As regards the first, the criteria laid down by Descartes, viz., clearness and distinctness, are unsatisfactory and ambiguous. It is evident that he implied under these clear and distinct recognition of necessity in the data or principles, but the nature of this necessity is never made clear.2 As regards the second, it was of importance to signalize, as against the scholastic view, that the universal in thought or reasoning was not only of the nature of the class notion, that genera and species were not the ultimate universals, but were themselves secondary products, formed by reasoning, and based upon essential connexion of facts. In this Descartes was but returning to the genuine Aristotelian doctrine, but his view has all the advantage derived from a truer and more scientific conception of what these connexions in nature really are.

Viewing logic as the doctrine which deals with the use and object of the intellectual faculties, Bacon divides it (in this approximating somewhat to the extended division of the Stoic logicians) into (1) the art of inquiry or invention, (2) the art of examination or judgment, (3) the art of memory, and (4) the art of elocution or tradition. The third and fourth divisions are unimportant ; the first and second might be called respectively the theory of the acquisition of knowledge and the theory of evidence or proof. The art of inquiry is subdivided into the art of the discovery of arts and the art of the discovery of arguments. The second of these Bacon regards as identical with the Topics of the Greek and Roman dialectic, and therefore as of comparatively slight value. Of the first there are two main branches : - (A) Experientia Litcrata and (B) Intcrprclatio .Naturx. The art of judgment has two subdivisions : - the examination of methods of reasoning - induction and syllogism - which resembles the older analytic ; and the examination of errors of reasoning - whether these be sophistical, i.e., the logical fallacies of the older doctrine, or errors of interpretation to be removed by careful criticism of scientific terms, or arising from erroneous tendences of the mind (the doctrine of idoM) - which resembles the older treatment of Elenehi.

The peculiarity of the Baconian logic, then, must be sought in the processes included under the all of discovering arts or knowledge. Among these the syllogism is not included. It is a process with no practical utility ; it involves premisses of which the truth is simply assumed, and consequently its conclusions can have no validity beyond that of the premisses ; it affects to determine the particular from the general, but in fact nature is much inore subtle than intellect, and our generalizations, which are but partial abstractions, arc quite inadequate to afford exhaustive knowledge of the particular ; it throws no light upon the essential part of cognition as a process in formation, viz., the method by which we are to obtain accurate notions of things, and judgments based on these notions. Moreover, the deductive or syllogistic procedure favours and encourages the tendency to rash generalization, to the formulation of a universal axiom from few particulars, and to the uncritical acceptance of experience. If syllogism exist at all, there must be a prior process, that of generalizing by rigid. and accurate methods from experience itself. Syllogism is not entirely worthless. It is of particular service in some branches of science (e.g., the mathematical), and generally may be employed so soon as the principles of a science are well established ; but it is a subordinate and secondary method.

The art of discovery, then, is the method of generalizing from experience. 'What this method shall be depends entirely on the thinker's conception of experience. Now Bacon's conception is perfectly definite. Observation presents to us complex natures which are the results of simpler, more general forms or causes. From the complex phenomena these forms arc to be sifted out by a methodical process of analysis and experiment. A general proposition is one stating the connexion between complex natures and their simple forms or causes ; it is, therefore, the result of a graduated process. No doubt there may be generalizations based only on an ingenious comparison of the complex phenomena as they are presented to us ; such a process Bacon calls Experientia Literata,, and the maxims recommended for it much resemble the ordinary methods of experiment, but truly scientific knowledge is only to be obtained by the complete inductive method. The characteristics of this inductive method follow at once from the nature of the object in view. The form which is sought can be detected only by examination of cases in which the given complex effect is present, in which it is absent, and in which it appears in different degrees or amounts. By a critical comparison of these cases we may be able to detect, and, were the enumeration exhaustive, we must infallibly detect, by process of exclusion or elimination, a phenomenon constaktly present when the effect is present, absent whenever the effect is absent, and varying in degree with the effect.. Such a phenomenon would be the form in question, - the cause of the given fact or attribute. Exhaustive enumeration is, of course, an ideal, and therefore the method of exclusion can never be perfectly carried out, but all additional aids have significance only as supplying in part the place of exhaustive enumeration. We may, on the basis of a wide examination, frame a first generalization (first vintage as Bacon metaphorically calls it), and proceed to test its correctness by carrying out the critical comparison with it in view. Or we may, under the guidance of our leading principle, take advantage of certain typical cases presented by nature, or force cases by experiment in such a way as to supersede the enumeration. There are prerogative instances, critical phenomena, helpful in discovery of the cause of a phenomenon. Of other aclminicula, or aids to induction, only the titles are given by Bacon, and it would be hazardous to conjecture as to their significance.3 The Baconian logic, then, or at least what is peculiar to it, is thoroughly conditioned by the peculiarities of the Baconian metaphysic or conception of nature and patina] processes. As to the novelty of the logic, this to us does not appear to lie in the mere fact that stress is laid upon induction, nor do we think it correct to assign to Bacon the introduction of the theory of induction as an integral portion of logic. But it consists in the new view taken of what constitutes the universal in thought, a view which may be inadequate, but which colours and affects every process of thought, and therefore every portion of logical theory. It is but a consequence of Bacon's narrow view of the essence of syllogism that be should set induction in opposition to deduction, and regard syllogism as of service only for communication of knowledge. His inductive methods am throughout syllogistic in this respect, that they like all processes of thought involve the combination of universal and particular. Experience is interpreted, that is to say, viewed under the light of a general idea or notion.